The product or quotient of a fortune and a debt is a debt. The ancient Greeks did not really address the problem of negative numbers, because their mathematics was founded on geometrical ideas.
Lengths, areas, and volumes resulting from geometrical constructions necessarily all had to be positive. Their proofs consisted of logical arguments based on the idea of magnitude. Magnitudes were represented by a line or an area, and not by a number like 4. In this way they could deal with 'awkward' numbers like square roots by representing them as a line.
For example, you can draw the diagonal of a square without having to measure it see note 2 below. Negative numbers did not begin to appear in Europe until the 15th century when scholars began to study and translate the ancient texts that had been recovered from Islamic and Byzantine sources. This began a process of building on ideas that had gone before, and the major spur to the development in mathematics was the problem of solving quadratic and cubic equations.
As we have seen, practical applications of mathematics often motivate new ideas and the negative number concept was kept alive as a useful device by the Franciscan friar Luca Pacioli - in his Summa published in , where he is credited with inventing double entry book-keeping. Free math problems solver! Member Login. Introduction Homepage Math blog Pre-algebra Pre-algebra lessons Algebra Algebra lessons Advanced algebra Geometry Geometry lessons Trigonometry lessons Math by grades Math by grade Math tests Online math tests Math vocabulary quizzes Applied mathematics Basic math word problems Algebra word problems Geometry word problems Consumer math Baseball math Math for nurses Statistics made easy Introduction to physics Interesting math topics Ancient numeration system Set notation Interesting math problems Math resources Other math websites Math worksheets Basic math formulas Basic math glossary Basic math calculator Geometry calculator Algebra solver Ask a math question Careers in math The Basic math blog.
History of negative numbers This is only a brief history of negative numbers. For a more comprehensive coverage and a longer reading, visit this site. For a concise, but right to the point introduction, stay right here with me. Looking for a book that will help you sharpen your basic algebra skills? Why were negative numbers considered with such suspicion? Why were they such an abstract concept? And how did they finally get accepted? I've not heard it yet, but I've been reliably informed that it was pretty good They even chat a bit about imaginary numbers too.
Register or Log In. The Magazine Shop. How can negative numbers exist? European mathematicians rejected negative numbers for ages. However, people in India and China have been using negative numbers for millennia. Eventually, the Europeans came around, and we use negative numbers everywhere today. Negative numbers make more sense if we look at a number line. On a number line, all the numbers to the right of zero are positive. If we move to the left of zero, they become negative:.
We end up with a negative number by subtracting a larger number from a smaller one. For example, if we subtract nine from eight, it looks like this:. There are plenty of other rules for using negative numbers in math. That may be true, but two negatives do make a positive! When we subtract a negative number, the subtraction sign is right next to the negative sign.
That means we can replace them with an addition sign. This rule also applies in multiplication. When we multiply two negative numbers, the answer is always positive:.
Negative numbers might seem mysterious in math problems. For many people, real-world negative numbers make more sense. Remember that cold morning when you read the thermometer? The negative numbers helped you understand how cold the weather was. Think of the thermometer as a number line. Have you ever studied maps or geography? If so, you may have heard of altitude. Altitude tells us how far above or below sea level a place is. For example, the peak of Mount Everest is 29, feet above sea level.
Badwater, California is the lowest point in the United States. Its altitude is feet! That means that if Badwater Basin were closer to the ocean, it would be under water.
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